Assertion : If the hypotenuse and an acute angle of one right triangle is equal to the hypotenuse and corresponding acute angle of another right triangle, then those two $Δ$ s are congruent.
Reason : By RHS property, the two right $Δ$ s are congruent.
Which of the following statements is correct?

A is true and R is the correct explanation of A.

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A is false and R is the correct explanation of A.

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A is false and R is false.

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None of these

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Solution

The correct option is B A is true and R is the correct explanation of A.
$∵$ Statement A is true by RHS property.

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Question 104

State whether the statement is True or False.

If the hypotenuse and an acute angle of one right-angled triangle are equal to the hypotenuse and an acute angle of another right-angled triangle, then the triangles are congruent.

Q. Which of the following statements are true and which of them are false?

(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two figures have equal areas, they are congruent.
(iv) If two triangles are equal in area, they are congruent.
(v) If two sides and one angle of a triangle are equal to the corresponding two sides and angle of another triangle, the triangle are congruent.
(vi) If two angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent.
(vii) If three angles of a triangle are equal to the corresponding angles of another triangle then the triangles are congruent.
(viii) If the hypotenuse and an acute angle of a right triangle are equal to the hypotenuse and the corresponding acute angle of another right triangle then the triangle are congruent.
(ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.
(x) If two triangles are congruent then their corresponding sides and their corresponding angles are congruent.

Q. Assertion : Two

Δ

s are said to be congruent if two sides and an angle of the one triangle are respectively equal to the two sides and an angle of the other triangle.
Reason: Two

Δ

s are congruent if two sides and the included angle of the one triangle are equal to the corresponding two sides and included angle of the other triangle.

Two statements A and R are given above. Which of the following statements is correct?

Q. Assertion: The circle drawn taking any one of the equal sides of an isosceles right triangle as diameter bisects the base.
Reason: The angle in a semicircle is 1 right angle.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Assertion: The sides of a $Δ A B C$ are in the ratio 2:3:4 and its perimeter is 36cm. Then, $a r (Δ A B C) = 12 \sqrt{15} c m^{2}$

Reason: If where a, b, c are the sides of a triangle, $\frac{s = (a + b + c)}{2}$ , then its area $= \sqrt{(s - a) (s - b) (s - c)}$

Which of the following is correct?

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Assertion : If the hypotenuse and an acute angle of one right triangle is equal to the hypotenuse and corresponding acute angle of another right triangle, then those two Δs are congruent.Reason : By RHS property, the two right Δs are congruent.Which of the following statements is correct?

The correct option is B A is true and R is the correct explanation of A.∵ Statement A is true by RHS property.

Assertion : If the hypotenuse and an acute angle of one right triangle is equal to the hypotenuse and corresponding acute angle of another right triangle, then those two $Δ$ s are congruent.
Reason : By RHS property, the two right $Δ$ s are congruent.
Which of the following statements is correct?

The correct option is B A is true and R is the correct explanation of A.
$∵$ Statement A is true by RHS property.